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A “wedge issue” is a controversial issue that creates a “wedge” between certain voters. A 19th century wedge issue was slavery; a 20th century wedge issue was abortion. “Wedge issue” has been cited in print since at least 1976. A “wedge issue” can also be described as a “hot-button issue” (since 1970).

Wikipedia: Wedge issue
A wedge issue is a social or political issue, often of a divisive or otherwise controversial nature, which splits apart or creates a “wedge” in the support base of one political group. Wedge issues can be advertised, publicly aired, and otherwise emphasized by an opposing political group, in an attempt to weaken the unity of the divided group, or to entice voters in the divided group to give their support to the opposing group. The use of wedge issues gives rise to wedge politics.

Wedge politics are the key to understanding the behavior of both candidates and voters during political campaigns. Among the voters most likely to be responsive to campaign information are those with conflicting predispositions—partisans who disagree with their party on a policy issue. For these cross-pressured partisans, campaign messages from the opposition can be persuasive if they are focused on the incongruent issue. Politicians look for wedge issues to emphasize in the campaign so that they can exploit the very tensions that create the opportunity for campaigns to “matter.” We argue that recent changes in the amount and type of information available about the mass public has increased the use of wedge politics and contributed to more fragmented and polarized issue agendas as candidates now micro-target different issue messages to different groups of voters in an effort to win over cross-pressured swing voters.
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Wedge politics in the United States
Both the Republican and Democratic parties have been accused of using social issues as wedge issues to divide the opposing voting base. For example, some Republican strategists have hoped that African Americans, a traditionally Democratic voting bloc, yet also one that possesses some of the most conservative views on matters of homosexuality, may be more inclined to vote for the Republican Party because of their opposition to gay marriage. Likewise, Democratic strategists have hoped that the issue of stem cell research could be used as a wedge issue against the right, since some Republicans support the research while others are morally opposed to the use of embryonic cells in research. In addition, the main difference between the Republican and Democratic platforms in the U.S. between 1992 and 2004 were the wedge issues of abortion and gay marriage, since each party sought to mobilize its base while having a common economic philosophy (of low taxes and support for big business and corporations) in an attempt to appeal to swing voters and win elections.

(Oxford English Dictionary)
wedge issue n. Polit. (orig. and chiefly N. Amer.) an extremely divisive issue, esp. viewed as a means of drawing voters away from a political party split by it.
1982 Chicago Tribune 13 May I. 23/5 It is Kennedy, today, who is promoting the high-visibility cause of the nuclear freeze, a *wedge issue if ever there was one.
1991 Newsweek 16 Dec. 28/3 Black is an expert in the use of ‘wedge issues’, like crime and the flag, to split off conservative white males from the Democratic Party.
1998 N.Y. Rev. Bks. 22 Oct. 74/1 The Croatian offensive proved to be a wedge issue that divided not only Americans and Europeans, but the top echelons of the American government itself.
2004 J. MICKLETHWAIT & A. WOOLDRIDGE Right Nation xii. 311 Conservatives were the first to turn abortion into a wedge issue in the South, as values trumped class in American politics.

Google BooksThe Coming of Post-Industrial Society:
A venture in social forecasting
By Daniel Bell
New York, NY: Basic Books
1976
Pg. LXXVI:
This is a move from a politics of exclusion to a politics of inclusion; in that respect, “affirmative action” has been a wedge issue in the political arena.

Google News Archive
17 October 1986, Beaver County Times (PA), “Southern Democrats hanging on to bridge issues” by David Broder, pg. A7, col. 2:
But more than that, education is the opposite of a wedge issue. It is a bridge issue for the diverse Democratic coalition.

New York (NY) Times
G.O.P. CHAIRMAN LEE ATWATER: PLAYING HARDBALL
By Eric Alterman; Eric Alterman, a senior fellow of the World Policy Institute, is writing a book on Washington pundits for Farrar, Straus & Giroux.
Published: April 30, 1989
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Atwater served notice on two occasions that the Horton furlough would be a central ‘’wedge’’ issue for the Republicans.

Google BooksDictionary of Politics:
Selected American and foreign political and legal terms
By Walter John Raymond
Lawrenceville, VA: Brunswick Pub. Corp.
1992
Pg. 560:
Wedge Issue. An issue or a problem, which divides voters in supporting a political candidate or a political party; an issue that divides a single constituency (e.g., the issue of abortion is a divisive issue around the world).

Google BooksAmerican Political Parties and Constitutional Politics
By Peter W. Schramm
Lanham, MD: Rowman & Littlefield
1993
Pg. 122:
Wedges
A “wedge” issue splits the opposition, causing a large share of its supporters to switch sides or withdraw from battle. Wedge issues have acquired a bad odor as critics of negative campaigning have attributed the concept to amoral political consultants. In fact, though, politicians have always used wedge issues—and often for honorable ends.

Google BooksSafire’s Political Dictionary
By William Safire
New York, NY: Oxford University Press
2008
Pg. 800:
wedge issue A HOT-BUTTON subject that splits a coalition or constituency.

“Education is the opposite of a wedge issue,” The Washington Post reported in the last month of the Reagan-Mondale campaign of 1984, which suggests the phrase’s appearance earlier. “It is a bridge issue for the diverse Democratic coalition.”
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The antonym of wedge issue is MAGNET ISSUE. See also BREAD-AND-BUTTER ISSUE; HOT BUTTON; ISSUES, THE; PARAMOUNT ISSUE; POCKETBOOK ISSUE.